Related papers: Stability Analysis in Magnetic Resonance Elastogra…
The shear-transformation-zone (STZ) theory of plastic deformation predicts that sufficiently soft, non-crystalline solids are linearly unstable against forming periodic arrays of microstructural shear bands. A limited nonlinear analysis…
In the perspective of developing smart hybrid materials with customized features, ferrogels and magnetorheological elastomers allow a synergy of elasticity and magnetism. The interplay between elastic and magnetic properties gives rise to a…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
Monitoring structures of elastic materials for defect detection by means of ultrasound waves (Structural Health Monitoring, SHM) demands for an efficient computation of parameters which characterize their mechanical behavior.…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
Complex fluids such as emulsions, colloidal gels, polymer or surfactant solutions are all characterized by the existence of a "microstructure" which may couple to an external flow on timescales that are easily probed in experiments. Such a…
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…
Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…
A new microscopic derivation of the elastic constants of amorphous solids is presented within the framework of nonaffine lattice dynamics, which makes use of a perturbative form of the low-frequency eigenvectors of the dynamical matrix…
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…
We consider the inverse problem of recovering stationary coefficients in a class of dynamical Schr\"odinger equations with locally analytic nonlinear terms. Upon treating the well-posedness for small initial data and trivial boundary data,…
In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the…
In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of…
In this work we calculate the local elastic moduli in a weakly polydisperse 2DLennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse grained microscopic expressions for the…